Question

To construct a quadrilateral uniquely, it is necessary to have the knowledge of a least ___________ independent elements.

• A. Four
• B. Five
• C. Three
• D. Six

Answer 1

Answer: (B)

Five

If the quadrilateral is irregular i.e it is not a rhombus or a parallelogram, then we need to know the lengths of all four sides plus one diagonal (i.e. at least five parts).

Example: For a quadrilateral $ABCD,$ if we know $AB=a,BC=b,CD=c,DA=d$ and $AC=k$ then we can construct the unique parallelogram subjected that

$a+b>k$ and $c+d>k$.

In fact we would construct two triangles $△ABC$ and $△ADC$ on common base $AC$, apexes $B$ and $D$ being on either side of $AC,$ using SSS method.